Numerical analysis of hyperbolic multi-phase flow using entropy stable schemes

Abstract

Nuclear power plants generate electricity through the steam power cycle so understanding the behaviour of the fluid is essential. This is done by studying the thermal hydraulics of the system which is governed by several conservation equations. These conservation equations cannot be solved analytically so instead one has to rely on numerical methods and computer codes to simulate the state of the system. In this thesis we look at two-phase systems where discontinuities are present and we see that standard and simple numerical methods such as finite volume schemes are not sufficient and yield unphysical results. Instead we take a different approach by studying entropy and path conditions of the system to create entropy stable path consistent schemes that are able to give a physical solution. We start from a standard two-fluid model and through several approximations we establish a two-phase system that is hyperbolic in nature. The pressure term in the system depends on the fluid and can therefore be expressed in multiple ways and in this thesis we study three ways to express the pressure. The first two ways are based on previously studied one-phase systems where the fluid is either in a pure liquid or gas phase. The last study of the pressure is expressed as an adiabatic process to give a more physical pressure expression which results in a pure two-phase expression that has previously not been studied. We design entropy stable schemes for these systems and test them on two scenarios to show how they react to two realistic discontinuities in the system. The results show that entropy stable schemes are able to handle discontinuities and converge towards a solution where other numerical methods were unsuccessful.